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"No rock is sentient. Some mammals are sentient. Hence, no mammal is a rock." I wrote a form and it's apparently wrong, but I don't get how.

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  • Do you have a textbook to review? There are clear written rules about how to handle syllogisms. In this case a fallacy is committed. You need to understand some concepts first to get this stuff. It is not common sense. You ask here because you don't understand the concepts in the textbook. There are generally 6 rules to know about syllogisms that would solve this for you. – Logikal Mar 10 at 3:56
  • I got it! The marking scheme was wrong and that confused me. Thought I was missing something. Thank you everyone still for helping out! – Randomo Mar 10 at 11:04
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Suppose that there is a Mammal (call it a) that is also a Rock.

By first premises, a is not Sentient.

Thus, a is a Mammal that is not Sentient.

But this does not contradict the second premise, that states that some (not necessarily all) Mammals are Sentient .


The logical form is:

No Rock is Sentient --- ¬∃x(Roc(x) and Sen(x))

Some mammals are sentient --- ∃x(Mam(x) and Sen(x))

Therefore: No mammal is a rock --- ¬∃x(Mam(x) and Roc(X)).

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"No rock is sentient. Some mammals are sentient. Hence, no mammal is a rock."

X = rocks

Y = sentient things

Z = mammals

No X are Z. Some Y are Z. Therefore, no Z are X.

Euler diagram looks like this:

╭─rocks─────╮     ╭─sentient things───╮
│           │     │                   │
│     ╭─────┼─────┼────╮              │
╰─────┼─────╯     ╰────┼──────────────╯
      │                │
      ╰──mammals───────╯

The "rocks" bubble and the "sentient things" bubble do not intersect as provided by the first premise. The "mammals" bubble intersects with the "sentient things" bubble as provided by the second premise. Nothing in the two premises says anything about whether the "mammals" bubble intersects the "rocks" bubble, so it may, making the conclusion invalid.

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    That's an Euler diagram. Venn diagrams also show the excluded options. – Sandejo Mar 9 at 22:13
  • @Sandejo ah yes, ty – causative Mar 9 at 23:15
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Suppose there are just two Mammals, one is a rock and the other is sentient, this satisfy the first two propositions, but contradicts your conclusion. If you read "thinking fast and slow" a great book by Daniel Kahneman, you would always want to Try and change the arguments into humanly relatable statements, an example of changing the arguments above and make it simpler to understand is :

No babies are quantum-physicists, some humans are quantum-physicists. now the conclusion " No humans are babies " is easily rejected.

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